How would the expression (x^2+1)(y^2+4) be rewritten using two squares?

I cannot think of another method rather than try them one by one.
D.
(x²+1)(y²2+4)=x²y²+y²+4x²+4
(xy-2)²+(2x+y)²=(x²y²-4xy+4)+(4x²+4xy+y²)=x²y²+4+4x²+y²

Try it this way:
since all the choices group xy and 2 together, we can regroup x²y²+y²+4x²+4 into 
(x²y²+4)+(y²+4x²)
=(x²y²+4-4xy)+(y²+4x²+4xy) or (x²y²+4+4xy)+(y²+4x²-4xy)
=(xy-2)²+(y+2x)² or (xy+2)²+(y-2x)²